## [1] 16
# dir01 <- here('s01') # agreggate data (no
# spatial diferences) dir1<-here('s1') # Data
# strata flishery dir2<-here('s2') # Same 9 with
# areas (SubStrata) as fleet. Dif size
# comoposition and dif CPUE and dif survey length
# and biomass data by strata dir3<-here('s3') #
# without S-R dir4<-here('s4') # dir5<-here('s5')
# # dir6<-here('s6') # dir7<-here('s7') # 2 set
# parametres EMM-2024/23 (Mardones)
# dir8<-here('s8') # s1 platoons dir9<-here('s9')
# # s1 w/ blocks
dir1.1 <- here("s1.1")  # sin predador ni ambiental
dir1.2 <- here("s1.2")  # s1.1 C/ predador
dir1.3 <- here("s1.3")  # s1.1 solo env
dir1.4 <- here("s1.4")  # s1.2 predator and env
Figs <- here("Figs")  # S

OVERVIEW

This study aims to evaluate the impact of ecosystem components—such as environmental variables and predator-prey interactions—on the productivity and key population dynamics of Euphausia superba in Subarea 48.1. By incorporating these factors into the assessment, we analyze how krill population variables respond to ecological variability, providing insights into their resilience and potential management implications.

Here, the reference model represents a baseline assessment of Euphausia superba population dynamics in Subarea 48.1, excluding environmental and ecological variables. This model assumes that krill productivity and population parameters are driven by intrinsic biological processes, such as growth, mortality, and recruitment and fishery impacts without accounting for external influences like environmental variability or predation pressure. By serving as a control scenario, this model provides a benchmark against which the impact of ecosystem components in productivity can be evaluated, allowing for a direct comparison of how environmental and ecological factors influence krill stock dynamics.

Statistical Model (SS3)

Stock Synthesis (v.3.30.21) is a widely used tool for assessing fish and invertebrate populations, including Antarctic krill. SS3 is implemented in C++ with estimation enabled through automatic differentiation (ADMB) (Fournier et al. 2012; Methot and Wetzel 2013). In this exercise, SS3 is configured as an integrated stock assessment model, explicitly accounting for age and size structure while incorporating key ecosystem drivers. The model simulates population processes such as growth, maturity, fecundity, recruitment, movement, and mortality, while also integrating environmental variability and predator-prey relationships to refine estimates of population trends. The analysis of model outputs is conducted using R, utilizing the r4ss and ss3diags packages (Taylor 2019; Winker et al. 2024). By leveraging a spatially implicit, ecosystem-informed approach, this assessment provides a robust framework for evaluating krill stock dynamics under changing environmental conditions. These insights are crucial for informing sustainable management strategies in the Antarctic Peninsula region, where krill plays a foundational role in the marine food web.

Parameters

The following table summarizes the key parameters to conditioning the reference model, including biological, growth, and population dynamics factors.

Input parameters for the initial SS3 model of krill. Each parameter line contains a minimum value (LO), maximum value (HI), and initial value (INIT). If the phase (PHASE) for the parameter is negative, the parameter is fixed as input
LO HI INIT PHASE
Natural Mortality
Nat M 0.20 1.00 0.270 -3
Growth
Lmin 0.00 5.00 3.400 -2
Lmax 1.00 10.00 5.000 -4
VonBert K 0.05 0.80 0.470 -4
CV young 0.05 0.25 0.140 -4
CV old 0.05 0.25 0.070 -4
relationship Length-Weigth
Wt a 0.00 3.00 0.000 -3
Wt b 1.00 4.00 3.347 -3
Maturity
L50% 0.20 5.00 1.800 -4
Mat slope -3.00 3.00 -2.900 -4
S-R relation
SR_LN(R0) 3.00 30.00 23.000 1
SR_BH_steep 0.20 1.00 0.850 -4
SR_sigmaR 0.00 2.00 1.200 -4
SR_regime -5.00 5.00 0.000 -4
SR_autocorr 0.00 0.00 0.000 -99
Catchability
LnQ_base_FISHERYBS(1) -25.00 25.00 -5.722 1
LnQ_base_FISHERYEI(2) -25.00 25.00 -5.722 1
Selectivity
SizeSel_P_1_FISHERYBS(1) 0.01 8.00 2.000 -3
SizeSel_P_2_FISHERYBS(1) 0.00 8.00 2.000 -2
SizeSel_P_1_FISHERYEI(2) 0.01 8.00 3.500 -3
SizeSel_P_2_FISHERYEI(2) 0.00 8.00 4.000 -2
SizeSel_P_1_FISHERYGS(3) 0.01 8.00 2.000 -3
SizeSel_P_2_FISHERYGS(3) 0.00 8.00 2.000 2
SizeSel_P_1_FISHERYJOIN(4) 0.01 8.00 3.500 -3
SizeSel_P_2_FISHERYJOIN(4) 0.00 8.00 2.000 -2
SizeSel_P_1_FISHERYSSIW(5) 0.01 8.00 3.500 -3
SizeSel_P_2_FISHERYSSIW(5) 0.00 8.00 2.000 -2
SizeSel_P_1_SURVEYBS(6) 1.00 7.00 2.000 -2
SizeSel_P_2_SURVEYBS(6) 1.00 7.00 1.000 -3
SizeSel_P_1_SURVEYEI(7) 1.00 7.00 3.000 -2
SizeSel_P_2_SURVEYEI(7) 1.00 7.00 1.000 -3
SizeSel_P_1_SURVEYGS(8) 1.00 7.00 2.000 -2
SizeSel_P_2_SURVEYGS(8) 1.00 7.00 1.000 -3
SizeSel_P_1_SURVEYJOIN(9) 1.00 7.00 3.000 2
SizeSel_P_2_SURVEYJOIN(9) 1.00 7.00 1.000 3
SizeSel_P_1_SURVEYSSIW(10) 1.00 7.00 2.000 -2
SizeSel_P_2_SURVEYSSIW(10) 1.00 7.00 1.000 -3
SizeSel_P_1_PREDATOR(11) 0.00 3.00 0.200 2
SizeSel_P_2_PREDATOR(11) 0.00 3.00 0.200 3

Source of data inpit

Scenarios

In Table 1 we have ten scenarios to test different option in modeling about main consideration in assessment of krill population.

Scenario Description
s1.1 Spatial data without environmental and predator components
s1.2 “s1.1” with predator components
s1.3 “s1.1” with environmental variable
s1.4 “s1.1” w/ both, predator fleet and environmental variable

Run Models

Data used en both (spatial and No spatial models) s1.1

and s1.4

RESULTS

Main Variables poulation in s1.1 scenario

Main Variables poulation in s1.2 scenario

Main Variables poulation in s1.3 scenario

Main Variables poulation in s1.4 scenario

Selectivity

Total biomass

Heatmap

hexagon

Diagnosis Base Model

A rigorous model diagnosis is essential to ensure the reliability and robustness of stock assessment models. The key steps for a good practice in model diagnosis include:

  1. Convergence Check: The model must reach a final convergence criterion of 1.0e-04 to ensure numerical stability and reliable parameter estimation.

  2. Residual Analysis: Both visual inspection and statistical metrics are used to evaluate model residuals, helping to detect patterns of bias or misfit.

  3. Retrospective Analysis: The Mohn’s rho parameter is used to assess the consistency of model estimates when sequentially removing recent years of data, identifying potential overestimation or underestimation trends.

  4. Likelihood Profile Analysis: This approach examines how the likelihood function behaves across a range of parameter values, providing insight into parameter uncertainty and model sensitivity.

This framework follows the recommendations outlined by Carvalho et al. (2021), aiming to enhance transparency and reproducibility in model evaluation.

Residual consistency

Residual analysis is a critical component of model diagnostics in stock assessments. It helps evaluate the fit of the model to observed data and detect potential biases or inconsistencies. This process is applied to both length composition data and abundance indices such as CPUE (Catch Per Unit Effort) and survey-derived estimates.

For length composition data, residuals represent the difference between observed and model-predicted length distributions. The standardized residuals are calculated as the difference between observed and expected proportions at each length bin. These residuals are plotted by year to identify systematic trends, biases, or inconsistencies in the data. Ideally, they should be randomly distributed around zero, indicating no systematic over- or underestimation.

For abundance indices such as CPUE and fishery-independent surveys, residuals are analyzed to assess model fit and potential sources of bias. Residuals are computed as the difference between observed index values and those predicted by the model, typically standardized by dividing by the standard error to facilitate comparison across years. These residuals are then plotted over time to evaluate trends. A shaded confidence region, like the green area in the provided plot, represents expected variability, with outliers highlighted in red or other distinct markers. Persistent positive or negative residuals may indicate systematic bias in the model or data collection process.

Statistical diagnostics are also performed to check for autocorrelation in residuals, which can indicate potential model misspecifications. When mean residual values are close to zero, the model fit is considered unbiased.

By integrating these residual analyses for both length and abundance indices, stock assessment models can be refined, improving their reliability and increasing confidence in the assessment results.

## 
##  Running Runs Test Diagnosics for Mean length 
## Plotting Residual Runs Tests

## 
## Runs Test stats by Mean length:
##         Index runs.p     test  sigma3.lo sigma3.hi type
## 1   FISHERYBS  0.218   Passed -0.1189633 0.1189633  len
## 2   FISHERYEI  0.013   Failed -0.2839347 0.2839347  len
## 3   FISHERYGS  0.912   Passed -0.1865475 0.1865475  len
## 4 FISHERYJOIN     NA Excluded         NA        NA  len
## 5 FISHERYSSIW  0.230   Passed -0.1176572 0.1176572  len
## 6    SURVEYBS  0.221   Passed -0.2220680 0.2220680  len
## 7    SURVEYEI  0.595   Passed -0.2119927 0.2119927  len
## 8    SURVEYGS  0.454   Passed -0.2928749 0.2928749  len
## 9  SURVEYJOIN  0.541   Passed -0.4156365 0.4156365  len
## 
##  Running Runs Test Diagnosics for Mean length 
## Plotting Residual Runs Tests

## 
## Runs Test stats by Mean length:
##          Index runs.p     test   sigma3.lo  sigma3.hi type
## 1    FISHERYBS  0.150   Passed -0.04986852 0.04986852  len
## 2    FISHERYEI  0.013   Failed -0.30357206 0.30357206  len
## 3    FISHERYGS  0.346   Passed -0.38742103 0.38742103  len
## 4  FISHERYJOIN     NA Excluded          NA         NA  len
## 5  FISHERYSSIW  0.230   Passed -0.14854188 0.14854188  len
## 6     SURVEYBS  0.001   Failed -0.29126384 0.29126384  len
## 7     SURVEYEI  0.627   Passed -0.22413735 0.22413735  len
## 8     SURVEYGS  0.409   Passed -0.35196215 0.35196215  len
## 9   SURVEYJOIN  0.500   Passed -0.44688062 0.44688062  len
## 10    PREDATOR  0.607   Passed -0.18346375 0.18346375  len
## 
##  Running Runs Test Diagnosics for Mean length 
## Plotting Residual Runs Tests

## 
## Runs Test stats by Mean length:
##         Index runs.p     test   sigma3.lo  sigma3.hi type
## 1   FISHERYBS  0.744   Passed -0.08525923 0.08525923  len
## 2   FISHERYEI  0.013   Failed -0.27984372 0.27984372  len
## 3   FISHERYGS  0.179   Passed -0.20160902 0.20160902  len
## 4 FISHERYJOIN     NA Excluded          NA         NA  len
## 5 FISHERYSSIW  0.230   Passed -0.12113187 0.12113187  len
## 6    SURVEYBS  0.631   Passed -0.22746036 0.22746036  len
## 7    SURVEYEI  0.786   Passed -0.18187931 0.18187931  len
## 8    SURVEYGS  0.136   Passed -0.29411566 0.29411566  len
## 9  SURVEYJOIN  0.500   Passed -0.41808588 0.41808588  len
## 
##  Running Runs Test Diagnosics for Mean length 
## Plotting Residual Runs Tests

## 
## Runs Test stats by Mean length:
##          Index runs.p     test   sigma3.lo  sigma3.hi type
## 1    FISHERYBS  0.500   Passed -0.04709602 0.04709602  len
## 2    FISHERYEI  0.013   Failed -0.27986404 0.27986404  len
## 3    FISHERYGS  0.013   Failed -0.26812009 0.26812009  len
## 4  FISHERYJOIN     NA Excluded          NA         NA  len
## 5  FISHERYSSIW  0.064   Passed -0.11843515 0.11843515  len
## 6     SURVEYBS  0.001   Failed -0.29845897 0.29845897  len
## 7     SURVEYEI  0.627   Passed -0.22182714 0.22182714  len
## 8     SURVEYGS  0.198   Passed -0.36195876 0.36195876  len
## 9   SURVEYJOIN  0.500   Passed -0.44265910 0.44265910  len
## 10    PREDATOR  0.607   Passed -0.26298700 0.26298700  len

Residual Analysis and RMSE

Residual analysis of mean length data is a fundamental diagnostic tool in stock assessments. It helps evaluate whether the model provides an unbiased fit to the observed data and detects potential biases over time. In this figure, mean length residuals are plotted across years, differentiated by data source, including fishery-dependent (FISHERY) and fishery-independent (SURVEY) datasets, as well as predator-related observations (PREDATOR). The residuals represent the deviation of observed mean length from model-predicted values, standardized to facilitate interpretation.

The black line represents a locally estimated scatterplot smoothing (Loess) curve, which provides a trend line to visualize systematic deviations over time. The presence of persistent positive or negative trends in the residuals may indicate biases in the growth model, selectivity assumptions, or misrepresentation of recruitment variability. The gray bars highlight periods where residual variability is particularly high, suggesting potential inconsistencies between observed and predicted size structures.

RMSE quantifies the overall deviation between observed and predicted values, providing an aggregate measure of model fit. Lower RMSE values indicate better agreement between observed and predicted data. In fisheries stock assessment (Hurtado-ferro et al. 2015), RMSE thresholds for acceptable model performance typically range between 10% and 30%, depending on the data quality and complexity of the population dynamics being modeled. Values exceeding this range suggest potential biases, requiring further investigation into the model structure, parameter estimation, or data sources.

By analyzing residual patterns and RMSE values, the model can be refined to improve the accuracy of mean length predictions, ultimately enhancing the reliability of stock assessment outcomes and management recommendations.

## Plotting JABBA residual plot
## 
## RMSE stats by Index:
##        indices RMSE.perc nobs
## 1    FISHERYBS       5.1   16
## 2    FISHERYEI      13.4   14
## 3    FISHERYGS       7.5   12
## 4  FISHERYJOIN       6.3    3
## 5  FISHERYSSIW       4.2   17
## 6     SURVEYBS       9.4   20
## 7     SURVEYEI       7.7   21
## 8     SURVEYGS      12.7   19
## 9   SURVEYJOIN      14.5   12
## 10    Combined       9.7  134
## Plotting JABBA residual plot
## 
## RMSE stats by Index:
##        indices RMSE.perc nobs
## 1    FISHERYBS       2.4   16
## 2    FISHERYEI      12.6   14
## 3    FISHERYGS      19.0   12
## 4  FISHERYJOIN       9.6    3
## 5  FISHERYSSIW       4.8   17
## 6     SURVEYBS      30.6   20
## 7     SURVEYEI      15.6   21
## 8     SURVEYGS      18.2   19
## 9   SURVEYJOIN      13.0   12
## 10    PREDATOR      13.5   29
## 11    Combined      16.6  163
## Plotting JABBA residual plot
## 
## RMSE stats by Index:
##        indices RMSE.perc nobs
## 1    FISHERYBS       4.9   16
## 2    FISHERYEI      13.9   14
## 3    FISHERYGS       9.4   12
## 4  FISHERYJOIN       7.3    3
## 5  FISHERYSSIW       4.4   17
## 6     SURVEYBS      15.0   20
## 7     SURVEYEI       7.6   21
## 8     SURVEYGS      11.9   19
## 9   SURVEYJOIN      14.2   12
## 10    Combined      10.7  134
## Plotting JABBA residual plot

## 
## RMSE stats by Index:
##        indices RMSE.perc nobs
## 1    FISHERYBS       1.6   16
## 2    FISHERYEI      12.4   14
## 3    FISHERYGS      18.3   12
## 4  FISHERYJOIN       8.1    3
## 5  FISHERYSSIW       3.9   17
## 6     SURVEYBS      30.4   20
## 7     SURVEYEI      15.3   21
## 8     SURVEYGS      18.3   19
## 9   SURVEYJOIN      12.6   12
## 10    PREDATOR      16.4   29
## 11    Combined      16.8  163
## Plotting JABBA residual plot
## 
## RMSE stats by Index:
##        indices RMSE.perc nobs
## 1    FISHERYBS      60.7   20
## 2    FISHERYEI      52.9   22
## 3    FISHERYGS      66.1   16
## 4  FISHERYJOIN      52.7    8
## 5  FISHERYSSIW      52.7   23
## 6     SURVEYBS      95.7   21
## 7     SURVEYEI      79.9   18
## 8     SURVEYGS     115.2   20
## 9   SURVEYJOIN     148.8    7
## 10  SURVEYSSIW      99.7    2
## 11    Combined      81.3  157
## Plotting JABBA residual plot
## 
## RMSE stats by Index:
##        indices RMSE.perc nobs
## 1    FISHERYBS      62.1   20
## 2    FISHERYEI      50.2   22
## 3    FISHERYGS      82.2   16
## 4  FISHERYJOIN      46.0    8
## 5  FISHERYSSIW      33.8   23
## 6     SURVEYBS     134.7   20
## 7     SURVEYEI      88.4   18
## 8     SURVEYGS      98.4   20
## 9   SURVEYJOIN     131.8    8
## 10  SURVEYSSIW     127.7    2
## 11    PREDATOR       NaN    0
## 12    Combined      85.7  157
## Plotting JABBA residual plot
## 
## RMSE stats by Index:
##        indices RMSE.perc nobs
## 1    FISHERYBS      63.7   20
## 2    FISHERYEI      50.0   22
## 3    FISHERYGS      70.3   16
## 4  FISHERYJOIN      46.2    8
## 5  FISHERYSSIW      50.1   23
## 6     SURVEYBS     121.9   20
## 7     SURVEYEI      94.3   18
## 8     SURVEYGS     119.7   21
## 9   SURVEYJOIN     123.7    7
## 10  SURVEYSSIW     131.0    2
## 11    Combined      87.0  157
## Plotting JABBA residual plot

## 
## RMSE stats by Index:
##        indices RMSE.perc nobs
## 1    FISHERYBS      62.5   20
## 2    FISHERYEI      48.2   22
## 3    FISHERYGS      81.0   16
## 4  FISHERYJOIN      42.1    8
## 5  FISHERYSSIW      32.8   23
## 6     SURVEYBS     127.5   20
## 7     SURVEYEI      91.5   18
## 8     SURVEYGS     112.8   21
## 9   SURVEYJOIN     129.3    8
## 10  SURVEYSSIW     132.7    2
## 11    PREDATOR       NaN    0
## 12    Combined      86.6  158

Comparision RMSE

##     Model1.1         Model1.2         Model1.3         Model1.4     
##  Min.   :0.5268   Min.   :0.3375   Min.   :0.4619   Min.   :0.3279  
##  1st Qu.:0.5480   1st Qu.:0.5314   1st Qu.:0.5347   1st Qu.:0.5176  
##  Median :0.7302   Median :0.8531   Median :0.8229   Median :0.8625  
##  Mean   :0.8826   Mean   :0.8969   Mean   :0.9325   Mean   :0.8845  
##  3rd Qu.:0.9867   3rd Qu.:1.2493   3rd Qu.:1.2814   3rd Qu.:1.2519  
##  Max.   :1.8820   Max.   :1.5809   Max.   :1.6408   Max.   :1.5163

##                               Df Sum Sq Mean Sq F value Pr(>F)
## rep(1:4, each = nrow(dfrmse))  1  0.001 0.00085   0.005  0.945
## Residuals                     38  6.638 0.17469
## 
##  Welch Two Sample t-test
## 
## data:  dfrmse$Model1.1 and dfrmse$Model1.2
## t = -0.07429, df = 17.971, p-value = 0.9416
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.4192226  0.3905904
## sample estimates:
## mean of x mean of y 
## 0.8825568 0.8968729
## 
##  Welch Two Sample t-test
## 
## data:  dfrmse$Model1.1 and dfrmse$Model1.3
## t = -0.25543, df = 17.998, p-value = 0.8013
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.4604222  0.3606026
## sample estimates:
## mean of x mean of y 
## 0.8825568 0.9324666
## 
##  Welch Two Sample t-test
## 
## data:  dfrmse$Model1.2 and dfrmse$Model1.3
## t = -0.18582, df = 17.985, p-value = 0.8547
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.4380513  0.3668639
## sample estimates:
## mean of x mean of y 
## 0.8968729 0.9324666
## 
##  Welch Two Sample t-test
## 
## data:  dfrmse$Model1.3 and dfrmse$Model1.4
## t = 0.25137, df = 17.978, p-value = 0.8044
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.3531612  0.4491482
## sample estimates:
## mean of x mean of y 
## 0.9324666 0.8844731
##                               Df Sum Sq Mean Sq F value Pr(>F)
## rep(1:4, each = nrow(dfrmse))  1  0.001 0.00085   0.005  0.945
## Residuals                     38  6.638 0.17469

This boxplot compares a summary of the Root Mean Square Error (RMSE) across four different models (s1.1, s1.2, s1.3, and s1.4) used to evaluate recruitment estimates of Antarctic krill. RMSE serves as an indicator of model accuracy, with lower values representing better predictive performance.

s1.1 exhibits the lowest median RMSE, suggesting it has the best overall fit among the four models. In contrast, Models 1.2, 1.3, and 1.4 show higher RMSE values, indicating comparatively lower predictive accuracy. The interquartile range (IQR) of these models is relatively similar, suggesting comparable variability in RMSE across models. Additionally, s1.1 has an outlier above 1.5 RMSE, which could indicate a case where the model’s predictions deviated significantly from observed values.

Overall, this analysis highlights that incorporating different environmental or predator-related variables in the models impacts their predictive ability. The differences in RMSE suggest that some models may overfit or underfit the recruitment patterns of krill, emphasizing the need to refine model selection based on ecological and statistical considerations.

Relationship Stock-Recruit

\[ R = \frac{aS}{1 + bS} \]

Where:
- \(S\) is the spawning stock biomass.
- \(R\) is the predicted recruitment.
- \(a\) is the maximum recruitment capacity.
- \(b\) regulates density dependence (higher values of \(b\) result in a lower plateau).

The blue line will show the asymptotic curve that describes the relationship between spawning stock biomass and recruitment.

Retrospective Analysis in Model Evaluation

Retrospective analyses provide insights into the differences in estimation patterns (underestimation or overestimation) among the models evaluated. These analyses assess the consistency and reliability of stock assessment models by systematically removing the most recent years of data and comparing the resulting estimates with the full dataset.

In this study, we conducted a retrospective analysis to examine the sensitivity of our recruitment and spawning stock biomass (SSB) estimates to the inclusion or exclusion of recent data. By applying this approach to multiple models, we identified potential biases and evaluated the stability of the recruitment estimates over time.

The retrospective patterns were assessed by calculating the relative error between the predictions of truncated datasets and the full dataset. These differences allowed us to detect trends in model performance, such as systematic overestimation or underestimation of key population parameters. Understanding these deviations is crucial for improving the robustness of the stock assessment models and ensuring more reliable projections for fisheries management.

Hindcast Cross-Validation and Prediction Skill

The Hindcast Cross-Validation (HCxval) diagnostic in Stock Synthesis is implemented using the model outputs generated by the r4ss::SS_doRetro() function. This diagnostic evaluates the predictive performance of the model by comparing hindcast predictions with observed data.

To assess prediction skill, we employ the Mean Absolute Scaled Error (MASE) as a robust metric. MASE is calculated by scaling the mean absolute error of the model predictions relative to the mean absolute error of a naïve baseline prediction. Specifically, the MASE score is computed as follows:

  • A MASE score greater than 1 indicates that the model’s average forecasts are less accurate than a random walk model.
  • A MASE score equal to 1 suggests that the model’s accuracy is similar to that of a random walk.
  • A MASE score less than 1 indicates that the model performs better than a random walk.
  • A MASE score of 0.5, for example, indicates that the model’s forecasts are twice as accurate as the naïve baseline prediction, suggesting the model has predictive skill.

This approach provides a rigorous evaluation of model forecasting capabilities and helps identify improvements for model calibration.

Kobe (status)

another

Rho parameter by model and quantity (SSB and F)
Model Quant Rho.type Rho.peel Rho.Rho Rho.ForcastRho
s1.1 SSB SSB 2019 -0.2970246 -0.2944080
s1.1 SSB SSB 2018 -0.2707308 -0.5103302
s1.1 SSB SSB 2017 -0.1872940 -0.3297243
s1.1 SSB SSB 2016 -0.1779392 -0.1957271
s1.1 SSB SSB Combined -0.2332471 -0.3325474
s1.1 F F 2019 1.1909249 2.5686552
s1.1 F F 2018 0.7828193 1.5773644
s1.1 F F 2017 0.8435982 1.0765231
s1.1 F F 2016 0.3245750 1.1174145
s1.1 F F Combined 0.7854794 1.5849893
s1.2 SSB SSB 2019 -0.0827150 -0.1016893
s1.2 SSB SSB 2018 -0.4893559 -0.5608395
s1.2 SSB SSB 2017 -0.7272409 -0.7935804
s1.2 SSB SSB 2016 -0.4875969 -0.8027882
s1.2 SSB SSB Combined -0.4467272 -0.5647244
s1.2 F F 2019 1.0251379 3.4863606
s1.2 F F 2018 1.0700408 3.1240360
s1.2 F F 2017 3.5165245 3.4961678
s1.2 F F 2016 0.8270261 5.1191803
s1.2 F F Combined 1.6096823 3.8064362
s1.3 SSB SSB 2019 -0.2631174 -0.3176714
s1.3 SSB SSB 2018 -0.3709787 -0.4678843
s1.3 SSB SSB 2017 -0.3342903 -0.5396513
s1.3 SSB SSB 2016 -0.3209827 -0.3946523
s1.3 SSB SSB Combined -0.3223423 -0.4299648
s1.3 F F 2019 1.1085776 2.9726497
s1.3 F F 2018 0.8449169 2.3280948
s1.3 F F 2017 1.3134959 2.0784872
s1.3 F F 2016 0.7604930 2.1222896
s1.3 F F Combined 1.0068708 2.3753803
s1.4 SSB SSB 2019 -0.1266622 -0.2006111
s1.4 SSB SSB 2018 -0.4523622 -0.6020788
s1.4 SSB SSB 2017 -0.6106873 -0.8405322
s1.4 SSB SSB 2016 -0.4535118 -0.7243463
s1.4 SSB SSB Combined -0.4108059 -0.5918921
s1.4 F F 2019 0.8803373 3.3155514
s1.4 F F 2018 0.8286323 3.1905901
s1.4 F F 2017 3.6632985 6.7126908
s1.4 F F 2016 0.4471872 14.4300252
s1.4 F F Combined 1.4548638 6.9122144

Likelihood tables

Likelihood Profile

SSplotProfile()

Convergence Criteria

The convergence criterion used for model calibration is set to a final threshold of 0.0001 (or equivalently 1.0e-04). This criterion defines the minimum acceptable difference between successive model iterations. Convergence is considered achieved when the absolute change in the objective function value or key parameters falls below this threshold. A smaller convergence value ensures that the model achieves a high degree of accuracy and stability in its final estimates, indicating that further iterations are unlikely to result in significant changes to the parameter estimates.

piner Plot

Outputs

Outputs Model s1.1

Main variables outputs from stock asssessment krill in WAP s1.1
Yr Era Seas Bio_all Bio_smry SpawnBio Recruit_0
1254 1989 VIRG 1 2184230 2176360 3565180 107962000
1255 1990 INIT 1 1498570 1490900 2259200 105278000
1256 1991 TIME 1 1498570 1490900 2259200 105278000
1257 1992 TIME 1 1616910 1609190 2452620 105844000
1258 1993 TIME 1 1723130 1715370 2661750 106370000
1259 1994 TIME 1 1814140 1806360 2839670 106759000
1260 1995 TIME 1 1889790 1881980 2987350 107049000
1261 1996 TIME 1 1951400 1943580 3107870 107266000
1262 1997 TIME 1 2000910 1993080 3204890 107430000
1263 1998 TIME 1 2031670 2031470 3280300 2722690
1264 1999 TIME 1 1950370 1950080 3329570 3861330
1265 2000 TIME 1 1709860 1703160 3365450 91895800
1266 2001 TIME 1 1523110 1504210 2802010 259242000
1267 2002 TIME 1 1638890 1627610 2264810 154705000
1268 2003 TIME 1 1971710 1971470 2294470 3332310
1269 2004 TIME 1 2079960 2078730 3317380 16879800
1270 2005 TIME 1 1916790 1913490 3747190 45270000
1271 2006 TIME 1 1724010 1708750 3238060 209287000
1272 2007 TIME 1 1640040 1631050 2612060 123361000
1273 2008 TIME 1 1833350 1832360 2343170 13566800
1274 2009 TIME 1 1869200 1864810 3037610 60221700
1275 2010 TIME 1 1731220 1719710 3226670 157914000
1276 2011 TIME 1 1606630 1586690 2567950 273609000
1277 2012 TIME 1 1905570 1872960 2385900 447447000
1278 2013 TIME 1 2520170 2519760 2744410 5517500
1279 2014 TIME 1 2918840 2914270 3602640 62737200
1280 2015 TIME 1 2758580 2740280 5255400 251086000
1281 2016 TIME 1 2672990 2619030 4425950 740188000
1282 2017 TIME 1 3269820 3269180 3819450 8874990
1283 2018 TIME 1 4057150 3997160 4289280 823040000
1284 2019 TIME 1 4780510 4672090 7517290 1487330000
1285 2020 TIME 1 6934500 6933840 6701380 8978140
1286 2021 FORE 1 8884260 8876160 10056300 111127000
1287 2022 FORE 1 8472730 8464580 16411100 111824000
1288 2023 FORE 1 7532870 7524730 14262700 111657000
1289 2024 FORE 1 6398190 6390070 11986300 111416000
1290 2025 FORE 1 5398930 5390840 9988720 111115000

Outputs Model s1.2

Main variables outputs from stock asssessment krill in WAP in s1.2
Yr Era Seas Bio_all Bio_smry SpawnBio Recruit_0
1354 1989 VIRG 1 2299170 2268860 2213450 415800000
1355 1990 INIT 1 2140700 2110590 1919210 413006000
1356 1991 TIME 1 2140700 2110590 1919210 413006000
1357 1992 TIME 1 2210510 2180300 2052100 414362000
1358 1993 TIME 1 2249080 2218830 2126300 415049000
1359 1994 TIME 1 2270970 2240690 2163880 415380000
1360 1995 TIME 1 2283380 2253090 2185490 415565000
1361 1996 TIME 1 2290340 2260040 2197820 415669000
1362 1997 TIME 1 2294230 2263930 2204700 415727000
1363 1998 TIME 1 2266810 2265650 2207770 15962500
1364 1999 TIME 1 1867210 1863690 2202490 48340700
1365 2000 TIME 1 1196690 1191800 2199340 67016200
1366 2001 TIME 1 828069 768871 1232060 812129000
1367 2002 TIME 1 1347830 1298870 737765 671607000
1368 2003 TIME 1 2369680 2367790 534842 25993000
1369 2004 TIME 1 2358800 2347400 2222130 156448000
1370 2005 TIME 1 1692350 1681210 2907030 152806000
1371 2006 TIME 1 1334460 1282450 1706020 713509000
1372 2007 TIME 1 1587260 1564820 1167630 307877000
1373 2008 TIME 1 2058080 2050430 968864 104953000
1374 2009 TIME 1 1799590 1784940 2225020 200938000
1375 2010 TIME 1 1401810 1386880 1981840 204876000
1376 2011 TIME 1 1141310 1130440 1172540 149095000
1377 2012 TIME 1 1076390 1042010 1058820 471730000
1378 2013 TIME 1 1258030 1225100 995034 451783000
1379 2014 TIME 1 1685050 1599720 774750 1170600000
1380 2015 TIME 1 2619570 2612840 1328470 92363200
1381 2016 TIME 1 2961350 2947640 1691030 188112000
1382 2017 TIME 1 2137730 2126280 3483620 157048000
1383 2018 TIME 1 1632790 1493160 2050430 1915550000
1384 2019 TIME 1 3002460 2903520 1450160 1357410000
1385 2020 TIME 1 5247580 5235720 1111080 162708000
1386 2021 FORE 1 5161170 5130090 5069530 426398000
1387 2022 FORE 1 3655000 3623850 5768290 427421000
1388 2023 FORE 1 2833070 2802300 3345400 422101000
1389 2024 FORE 1 2415010 2384550 2502690 417931000
1390 2025 FORE 1 2214670 2184410 2127620 415061000

Outputs Model s1.3

Main variables outputs from stock asssessment krill in WAP in s1.3
Yr Era Seas Bio_all Bio_smry SpawnBio Recruit_0
1305 1989 VIRG 1 1354540 1349660 2210920 66952200
1306 1990 INIT 1 925937 921186 1367470 65178600
1307 1991 TIME 1 925937 921186 1367470 65178600
1308 1992 TIME 1 1012370 1007590 1539740 65688900
1309 1993 TIME 1 1082790 1077970 1679460 66030400
1310 1994 TIME 1 1139590 1134760 1789740 66264200
1311 1995 TIME 1 1184920 1180070 1878070 66432800
1312 1996 TIME 1 1220820 1215970 1948280 66556400
1313 1997 TIME 1 1249200 1244350 2003870 66648400
1314 1998 TIME 1 1266420 1266130 2046680 3933970
1315 1999 TIME 1 1216010 1215500 2071380 7024060
1316 2000 TIME 1 1072540 1067770 2089420 65411200
1317 2001 TIME 1 972011 956267 1743630 215989000
1318 2002 TIME 1 1109210 1100090 1431580 125160000
1319 2003 TIME 1 1429620 1429580 1495100 561097
1320 2004 TIME 1 1554480 1552980 2429710 20540100
1321 2005 TIME 1 1457100 1454260 2840910 39008600
1322 2006 TIME 1 1336990 1324330 2463950 173714000
1323 2007 TIME 1 1281790 1274680 2002810 97556700
1324 2008 TIME 1 1457730 1456870 1826580 11786600
1325 2009 TIME 1 1495420 1492040 2433300 46468300
1326 2010 TIME 1 1380600 1374330 2577450 86071200
1327 2011 TIME 1 1216340 1201580 2007830 202457000
1328 2012 TIME 1 1370300 1353670 1857780 228170000
1329 2013 TIME 1 1695430 1695250 1914900 2452510
1330 2014 TIME 1 1790520 1786460 2457000 55652700
1331 2015 TIME 1 1629480 1613420 3067990 220458000
1332 2016 TIME 1 1591680 1567250 2434430 335175000
1333 2017 TIME 1 1924560 1917300 2100330 99619900
1334 2018 TIME 1 2324930 2262040 2686920 862770000
1335 2019 TIME 1 3241680 3138230 3990880 1419210000
1336 2020 TIME 1 5615900 5614770 4015250 15552100
1337 2021 FORE 1 7713090 7708050 8063680 69167000
1338 2022 FORE 1 7512020 7506950 14559700 69554800
1339 2023 FORE 1 6671280 6666210 12838900 69490000
1340 2024 FORE 1 5619480 5614420 10736700 69382900
1341 2025 FORE 1 4656920 4651870 8812160 69240500

Outputs Model s1.4

Main variables outputs from stock asssessment krill in WAP in s1.4
Yr Era Seas Bio_all Bio_smry SpawnBio Recruit_0
1305 1989 VIRG 1 1354540 1349660 2210920 66952200
1306 1990 INIT 1 925937 921186 1367470 65178600
1307 1991 TIME 1 925937 921186 1367470 65178600
1308 1992 TIME 1 1012370 1007590 1539740 65688900
1309 1993 TIME 1 1082790 1077970 1679460 66030400
1310 1994 TIME 1 1139590 1134760 1789740 66264200
1311 1995 TIME 1 1184920 1180070 1878070 66432800
1312 1996 TIME 1 1220820 1215970 1948280 66556400
1313 1997 TIME 1 1249200 1244350 2003870 66648400
1314 1998 TIME 1 1266420 1266130 2046680 3933970
1315 1999 TIME 1 1216010 1215500 2071380 7024060
1316 2000 TIME 1 1072540 1067770 2089420 65411200
1317 2001 TIME 1 972011 956267 1743630 215989000
1318 2002 TIME 1 1109210 1100090 1431580 125160000
1319 2003 TIME 1 1429620 1429580 1495100 561097
1320 2004 TIME 1 1554480 1552980 2429710 20540100
1321 2005 TIME 1 1457100 1454260 2840910 39008600
1322 2006 TIME 1 1336990 1324330 2463950 173714000
1323 2007 TIME 1 1281790 1274680 2002810 97556700
1324 2008 TIME 1 1457730 1456870 1826580 11786600
1325 2009 TIME 1 1495420 1492040 2433300 46468300
1326 2010 TIME 1 1380600 1374330 2577450 86071200
1327 2011 TIME 1 1216340 1201580 2007830 202457000
1328 2012 TIME 1 1370300 1353670 1857780 228170000
1329 2013 TIME 1 1695430 1695250 1914900 2452510
1330 2014 TIME 1 1790520 1786460 2457000 55652700
1331 2015 TIME 1 1629480 1613420 3067990 220458000
1332 2016 TIME 1 1591680 1567250 2434430 335175000
1333 2017 TIME 1 1924560 1917300 2100330 99619900
1334 2018 TIME 1 2324930 2262040 2686920 862770000
1335 2019 TIME 1 3241680 3138230 3990880 1419210000
1336 2020 TIME 1 5615900 5614770 4015250 15552100
1337 2021 FORE 1 7713090 7708050 8063680 69167000
1338 2022 FORE 1 7512020 7506950 14559700 69554800
1339 2023 FORE 1 6671280 6666210 12838900 69490000
1340 2024 FORE 1 5619480 5614420 10736700 69382900
1341 2025 FORE 1 4656920 4651870 8812160 69240500

Comparison

Comparison outputs betwwen scenarios

Comparison between select models Ref Model: No Env-Predator and S1.1 w/ Env and Predator data

Comparsion in sd long term time series

Autocorrelation in Recruit

To evaluate the temporal correlation structure of krill recruitment under different model configurations, we performed an Autocorrelation Function (ACF) analysis. The ACF measures the correlation between observations at different time lags, helping to assess whether recruitment estimates exhibit persistence or randomness across time.

The analysis was conducted on recruitment estimates derived from four model scenarios:

A reference model without environmental or predator influences (Ref Model: No Env-Predator). A model incorporating predator data (S1.1 w/ Predator data). A model incorporating environmental data (S1.1 w/ Env data). A model incorporating both environmental and predator data (S1.1 w/ Env and Predator data). Each model’s residuals were extracted, and the autocorrelation function (ACF) was computed for a time lag range of up to 15 years. The dashed blue lines in the plots represent the 95% confidence intervals, indicating the threshold beyond which correlation values are statistically significant. If autocorrelation values remain within this range, it suggests that the recruitment estimates behave as a random process with no significant dependence on past values. Conversely, autocorrelation values exceeding these bounds indicate recruitment persistence or cyclic patterns.

The ACF plots indicate that the reference model (without environmental or predator data) exhibits weak but noticeable positive autocorrelation at certain lags, suggesting some degree of recruitment dependence over time. However, this autocorrelation does not appear strong or systematic.

The model incorporating only predator data shows a slight reduction in autocorrelation magnitude, suggesting that predator-driven recruitment variability may have captured part of the temporal structure in the data.

The model with only environmental data exhibits a further reduction in autocorrelation, implying that environmental variability explains a larger portion of recruitment trends than predator effects alone.

Finally, the model that includes both environmental and predator data presents the lowest autocorrelation values, with nearly all bars remaining within the confidence bounds. This suggests that incorporating both factors provides the most effective explanation of recruitment fluctuations, reducing unexplained temporal structure.

Overall, these results indicate that recruitment variability is at least partially driven by environmental and predator influences, and models integrating these factors provide more robust and independent recruitment estimates, minimizing systematic dependencies over time.

Recruit deviation

Platoons analisis

### AKL

In a catch-at-length model like krill assessment the AKL matrix is modelled trought parametrization process

Representation of ALK Matrix to krill in 48.1

Representation of ALK Matrix to krill in 48.1

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